Theorems · Theorem · measure theory

MeasureTheory.integral_mono_measure

∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} [inst_2 : PartialOrder E] [IsOrderedAddMonoid E] [IsOrderedModule ℝ E]
  [OrderClosedTopology E] {f : α → E} {ν : MeasureTheory.Measure α},
  μ ≤ ν → 0 ≤ᵐ[ν] f → MeasureTheory.Integrable f ν → ∫ (a : α), f a ∂μ ≤ ∫ (a : α), f a ∂ν

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

5 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpacePartialOrderIsOrderedAddMonoidIsOrderedModuleOrderClosedTopology